2 Answers
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The ISS orbit is prograde - in the direction of the Earth rotation. Prograde orbits are orbits with inclination less than 90 degrees. ISS inclination is 51.6 degrees.

These orbits are slightly easier to reach, because they don't require as much fuel, as you get additional "kick" from the Earth during launch. Retrograde (opposite direction) orbits are rare, because they require more fuel to reach. It would be inefficient to build the ISS in retrograde orbit, because all the craft would have to spend additional fuel to get there. The ISS orbit was chosen to make it accessible from the key launch sites in United States (Florida) and Kazakhstan (Baikonur).

There's only one space launch site in the world that I know of that regularly launches satellites into retrograde orbits and that's the Israeli launch site of Palmachim. They launch retrograde mostly due to the hostile relations between Israel and it's neighboring countries to the east, and a rocket carrying a satellite can very very difficult to distinguish from a rocket carrying a warhead, especially if you're trying to figure it out after it's launched and is heading (potentially) towards you.
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NickolaiMar 24 '14 at 14:05

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Actually, it is very easy to differentiate between them. They fly VERY different trajectories, with VERY different motor burn profiles. Orbit identification from a small number of observations used to be a routine undergraduate astrodynamics computer programming homework problem. (See [Bate, Mueller, White] "Fundamentals of Astrodynamics", Dover Books, for more details.)
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John R. StrohmMar 24 '14 at 20:52

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Agreed, but when you are the neighboring country an actual missile would have a rather short flight time. The reply would have to be fired very quickly - you won't have enough time to watch the burn profile and determine it is actually hostile before it hits you. Launching out to sea sounds sensible.
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paulOct 25 '14 at 0:40

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@Nickolai Actually, Vandenberg AFB often launches spacecraft into sun-synchronous orbits, which, at a typical inclination of about 98 degrees, are ever so slightly retrograde.
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TristanMar 10 at 14:24

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Low Earth Orbit (LEO) is typically 100 nmi above nominal Mean Sea Level. A launch vehicle attempting to reach LEO must reach that altitude with zero vertical velocity component at that time, and orbital velocity horizontal component. ICBM apogees are typically several times that altitude, with almost zero horizontal velocity component at apogee, meaning the payload/warhead starts falling back to Earth (hence the term "ballistic"). You look at the flight path, seeing whether it is pitching over and accelerating to orbital velocity in horizontal.
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John R. StrohmMar 13 at 11:58

It orbits same direction as Earth. You can expect all space stations always to be build to orbit in direction of earth. Saves fuel to reach them since you get extra boost while leaving Earth and less full again when slowing down when reaching the station. If it would rotate against earth the speed would be twice as night relative to you and you would need to spend more power to slow down. Or if you would chase it lose the extra boost leaving earth and waist there no fuel.

This is not correct. Launching prograde (in direction of Earth's rotation) saves ~ 465 m/s to orbital velocity, if launched with 0° inclination from equator. That changes a bit if you launch to ISS inclination of 51.65°. From Baikonur, where most launches to the ISS happen nowadays, you'd save about 321.5 m/s. Orbital speed of the station is roughly 7,660 m/s. So Earth's rotation would only have helped ~ 4.2%, if we didn't count atmospheric drag, and ~ 3.3-3.5% since we have to.
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TildalWave♦Apr 30 at 22:11